Poisson reduction and branes in Poisson-Sigma models

We analyse the problem of boundary conditions for the Poisson-Sigma model and extend previous results showing that non-coisotropic branes are allowed. We discuss the canonical reduction of a Poisson structure to a submanifold, leading to a Poisson algebra that generalizes Dirac’s construction. The phase space of the model on the strip is related to the (generalized) Dirac bracket on the branes through a dual pair structure.